cipherbreak.py

   1 """A set of functions to break the ciphers give in ciphers.py.
   2 """
   3
   4 import string
   5 import collections
   6 import norms
   7 import logging
   8 import math
   9
  10 import matplotlib.pyplot as plt
  11
  12 logger = logging.getLogger(__name__)
  13 logger.addHandler(logging.FileHandler('cipher.log'))
  14 logger.setLevel(logging.WARNING)
  15 #logger.setLevel(logging.INFO)
  16 #logger.setLevel(logging.DEBUG)
  17
  18 from cipher import *
  19 from language_models import *
  20
  21 # To time a run:
  22 #
  23 # import timeit
  24 # c5a = open('2012/5a.ciphertext', 'r').read()
  25 # timeit.timeit('keyword_break(c5a)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break', number=1)
  26 # timeit.repeat('keyword_break_mp(c5a, chunksize=500)', setup='gc.enable() ; from __main__ import c5a ; from cipher import keyword_break_mp', repeat=5, number=1)
  27
  28
  29 def frequencies(text):
  30     """Count the number of occurrences of each character in text
  31
  32     >>> sorted(frequencies('abcdefabc').items())
  33     [('a', 2), ('b', 2), ('c', 2), ('d', 1), ('e', 1), ('f', 1)]
  34     >>> sorted(frequencies('the quick brown fox jumped over the lazy ' \
  35          'dog').items()) # doctest: +NORMALIZE_WHITESPACE
  36     [(' ', 8), ('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1),
  37      ('g', 1), ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1),
  38      ('n', 1), ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2),
  39      ('v', 1), ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  40     >>> sorted(frequencies('The Quick BROWN fox jumped! over... the ' \
  41          '(9lazy) DOG').items()) # doctest: +NORMALIZE_WHITESPACE
  42     [(' ', 8), ('!', 1), ('(', 1), (')', 1), ('.', 3), ('9', 1), ('B', 1),
  43      ('D', 1), ('G', 1), ('N', 1), ('O', 2), ('Q', 1), ('R', 1), ('T', 1),
  44      ('W', 1), ('a', 1), ('c', 1), ('d', 1), ('e', 4), ('f', 1), ('h', 2),
  45      ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('o', 2), ('p', 1),
  46      ('r', 1), ('t', 1), ('u', 2), ('v', 1), ('x', 1), ('y', 1), ('z', 1)]
  47     >>> sorted(frequencies(sanitise('The Quick BROWN fox jumped! over... '\
  48          'the (9lazy) DOG')).items()) # doctest: +NORMALIZE_WHITESPACE
  49     [('a', 1), ('b', 1), ('c', 1), ('d', 2), ('e', 4), ('f', 1), ('g', 1),
  50      ('h', 2), ('i', 1), ('j', 1), ('k', 1), ('l', 1), ('m', 1), ('n', 1),
  51      ('o', 4), ('p', 1), ('q', 1), ('r', 2), ('t', 2), ('u', 2), ('v', 1),
  52      ('w', 1), ('x', 1), ('y', 1), ('z', 1)]
  53     >>> frequencies('abcdefabcdef')['x']
  54     0
  55     """
  56     return collections.Counter(c for c in text)
  57
  58
  59 def caesar_break(message, fitness=Pletters):
  60     """Breaks a Caesar cipher using frequency analysis
  61
  62     >>> caesar_break('ibxcsyorsaqcheyklxivoexlevmrimwxsfiqevvmihrsasrxliwyrh' \
  63           'ecjsppsamrkwleppfmergefifvmhixscsymjcsyqeoixlm') # doctest: +ELLIPSIS
  64     (4, -130.849989015...)
  65     >>> caesar_break('wxwmaxdgheetgwuxztgptedbgznitgwwhpguxyhkxbmhvvtlbhgtee' \
  66           'raxlmhiixweblmxgxwmhmaxybkbgztgwztsxwbgmxgmert') # doctest: +ELLIPSIS
  67     (19, -128.82410410...)
  68     >>> caesar_break('yltbbqnqnzvguvaxurorgenafsbezqvagbnornfgsbevpnaabjurer' \
  69           'svaquvzyvxrnznazlybequrvfohgriraabjtbaruraprur') # doctest: +ELLIPSIS
  70     (13, -126.25403935...)
  71     """
  72     sanitised_message = sanitise(message)
  73     best_shift = 0
  74     best_fit = float('-inf')
  75     for shift in range(26):
  76         plaintext = caesar_decipher(sanitised_message, shift)
  77         fit = fitness(plaintext)
  78         logger.debug('Caesar break attempt using key {0} gives fit of {1} '
  79                      'and decrypt starting: {2}'.format(shift, fit,
  80                                                         plaintext[:50]))
  81         if fit > best_fit:
  82             best_fit = fit
  83             best_shift = shift
  84     logger.info('Caesar break best fit: key {0} gives fit of {1} and '
  85                 'decrypt starting: {2}'.format(best_shift, best_fit,
  86                     caesar_decipher(sanitised_message, best_shift)[:50]))
  87     return best_shift, best_fit
  88
  89 def affine_break(message, fitness=Pletters):
  90     """Breaks an affine cipher using frequency analysis
  91
  92     >>> affine_break('lmyfu bkuusd dyfaxw claol psfaom jfasd snsfg jfaoe ls ' \
  93           'omytd jlaxe mh jm bfmibj umis hfsul axubafkjamx. ls kffkxwsd jls ' \
  94           'ofgbjmwfkiu olfmxmtmwaokttg jlsx ls kffkxwsd jlsi zg tsxwjl. jlsx ' \
  95           'ls umfjsd jlsi zg hfsqysxog. ls dmmdtsd mx jls bats mh bkbsf. ls ' \
  96           'bfmctsd kfmyxd jls lyj, mztanamyu xmc jm clm cku tmmeaxw kj lai ' \
  97           'kxd clm ckuxj.') # doctest: +ELLIPSIS
  98     ((15, 22, True), -340.601181913...)
  99     """
 100     sanitised_message = sanitise(message)
 101     best_multiplier = 0
 102     best_adder = 0
 103     best_one_based = True
 104     best_fit = float("-inf")
 105     for one_based in [True, False]:
 106         for multiplier in [x for x in range(1, 26, 2) if x != 13]:
 107             for adder in range(26):
 108                 plaintext = affine_decipher(sanitised_message,
 109                                             multiplier, adder, one_based)
 110                 fit = fitness(plaintext)
 111                 logger.debug('Affine break attempt using key {0}x+{1} ({2}) '
 112                              'gives fit of {3} and decrypt starting: {4}'.
 113                              format(multiplier, adder, one_based, fit,
 114                                     plaintext[:50]))
 115                 if fit > best_fit:
 116                     best_fit = fit
 117                     best_multiplier = multiplier
 118                     best_adder = adder
 119                     best_one_based = one_based
 120     logger.info('Affine break best fit with key {0}x+{1} ({2}) gives fit of '
 121                 '{3} and decrypt starting: {4}'.format(
 122                     best_multiplier, best_adder, best_one_based, best_fit,
 123                     affine_decipher(sanitised_message, best_multiplier,
 124                                     best_adder, best_one_based)[:50]))
 125     return (best_multiplier, best_adder, best_one_based), best_fit
 126
 127
 128 def plot_frequency_histogram(freqs, sort_key=None):
 129     x = range(len(freqs.keys()))
 130     y = [freqs[l] for l in sorted(freqs.keys(), key=sort_key)]
 131     f = plt.figure()
 132     ax = f.add_axes([0.1, 0.1, 0.9, 0.9])
 133     ax.bar(x, y, align='center')
 134     ax.set_xticks(x)
 135     ax.set_xticklabels(sorted(freqs.keys(), key=sort_key))
 136     f.show()
 137
 138
 139 if __name__ == "__main__":
 140     import doctest
 141     doctest.testmod()